Total Questions:50 Total Time: 75 Min
Remaining:
Question:The centre of the conic represented by the equation \(2{x^2} - 72xy + 23{y^2} - 4x - 28y - 48 = 0\) is
\(\left( {\frac{{11}}{{15}},\;\frac{2}{{25}}} \right)\)
\(\left( {\frac{2}{{25}},\;\frac{{11}}{{25}}} \right)\)
\(\left( {\frac{{11}}{{15}},\; - \frac{2}{{25}}} \right)\)
\(\left( { - \frac{{11}}{{25}},\; - \frac{2}{{25}}} \right)\)
Question:The centre of \(14{x^2} - 4xy + 11{y^2} - 44x - 58y + 71 = 0\)
(2, 3)
(2, – 3)
(– 2, 3)
(– 2, – 3)
Question:A parabola passing through the point \(( - 4,\; - 2)\) has its vertex at the origin and y-axis as its axis. The latus rectum of the parabola is
6
8
10
12
Question:The focus of the parabola \({x^2} = - 16y\) is
(4, 0)
(0, 4)
(–4, 0)
(0, –4)
Question:The equation of the latus rectum of the parabola \({x^2} + 4x + 2y = 0\) is
\(2y + 3 = 0\)
\(3y = 2\)
\(2y = 3\)
\(3y + 2 = 0\)
Question:Vertex of the parabola \(9{x^2} - 6x + 36y + 9 = 0\) is
\((1/3,\; - 2/9)\)
\(( - 1/3,\; - 1/2)\)
\(( - 1/3,\;1/2)\)
\((1/3,\;1/2)\)
Question:The length of the latus rectum of the parabola \(9{x^2} - 6x + 36y + 19 = 0\)
36
9
4
Question:The axis of the parabola \(9{y^2} - 16x - 12y - 57 = 0\) is
\(x + 3y = 3\)\(2x = 3\)
\(y = 3\)
None of these
Question:The length of the latus rectum of the parabola \({x^2} - 4x - 8y + 12 = 0\) is
Question:The focus of the parabola \(y = 2{x^2} + x\) is
(0, 0)
\(\left( {\frac{1}{2},\;\frac{1}{4}} \right)\)
\(\left( { - \frac{1}{4},\;0} \right)\)
\(\left( { - \frac{1}{4},\;\frac{1}{8}} \right)\)
Question:The point of contact of the tangent \(18x - 6y + 1 = 0\) to the parabola \({y^2} = 2x\)is
\(\left( {\frac{{ - 1}}{{18}},\;\frac{{ - 1}}{3}} \right)\)
\(\left( {\frac{{ - 1}}{{18}},\;\frac{1}{3}} \right)\)
\(\left( {\frac{1}{{18}},\;\frac{{ - 1}}{3}} \right)\)
\(\left( {\frac{1}{{18}},\;\frac{1}{3}} \right)\)
Question:The equation of the common tangent of the parabolas \({x^2} = 108y\) and \({y^2} = 32x\), is
\(2x + 3y = 36\)
\(2x + 3y + 36 = 0\)
\(3x + 2y = 36\)
\(3x + 2y + 36 = 0\)
Question:The angle between the tangents drawn at the end points of the latus rectum of parabola \({y^2} = 4ax\), is
\(\frac{\pi }{3}\)
\(\frac{{2\pi }}{3}\)
\(\frac{\pi }{4}\)
\(\frac{\pi }{2}\)
Question:The line \(y = mx + c\) touches the parabola \({x^2} = 4ay\), if
\(c = - am\)
\(c = - a/m\)
\(c = - a{m^2}\)
\(c = a/{m^2}\)
Question:If \(lx + my + n = 0\) is tangent to the parabola \({x^2} = y\), then condition of tangency is
\({l^2} = 2mn\)
\(l = 4{m^2}{n^2}\)
\({m^2} = 4\ln \)
\({l^2} = 4mn\)
Question:The equation of the tangent to the parabola \({y^2} = 9x\) which goes through the point (4, 10), is
\(x + 4y + 1 = 0\)
\(9x + 4y + 4 = 0\)
\(x - 4y + 36 = 0\)
\(9x - 4y + 4 = 0\)
3 and 4 are correct
Question:The point on the parabola \({y^2} = 8x\) at which the normal is inclined at 60o to the x-axis has the co-ordinates
\((6,\; - 4\sqrt 3 )\)
\((6,\;4\sqrt 3 )\)
\(( - 6,\; - 4\sqrt 3 )\)
\(( - 6,\;4\sqrt 3 )\)
Question:The slope of the normal at the point \((a{t^2},\;2at)\) of the parabola \({y^2} = 4ax\), is
\(\frac{1}{t}\)
t
\( - \frac{1}{t}\)
Question:Equation of any normal to the parabola \({y^2} = 4a(x - a)\) is
\(y = mx - 2am - a{m^3}\)
\(y = m\,(x + a) - 2am - a{m^3}\)
\(y = m\,(x - a) + \frac{a}{m}\)
\(y = m\,(x - a) - 2am - a{m^3}\)
Question:Tangents drawn at the ends of any focal chord of a parabola \({y^2} = 4ax\) intersect in the line
\(y - a = 0\)
\(y + a = 0\)
\(x - a = 0\)
\(x + a = 0\)
Question:For the above problem, the area of triangle formed by chord of contact and the tangents is given by
\(8\sqrt 3 \)
\(8\sqrt 2 \)
Question:The point on parabola \(2y = {x^2}\), which is nearest to the point (0, 3) is
(\( \pm \) 4, 8)
\(( \pm 1,\,1/2)\)
(\( \pm \) 2, 2)
Question:The equation of the ellipse whose centre is at origin and which passes through the points (-3, 1) and (2, -2) is
\(5{x^2} + 3{y^2} = 32\)
\(3{x^2} + 5{y^2} = 32\)
\(5{x^2} - 3{y^2} = 32\)
\(3{x^2} + 5{y^2} + 32 = 0\)
Question:If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is
39/4
15
37/2
Question:The lengths of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along the y-axis. The equation of the ellipse referred to its centre as origin is
\(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1\)
\(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1\)
\(\frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{64}} = 1\)
\(\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{100}} = 1\)
Question:If the centre, one of the foci and semi-major axis of an ellipse be (0, 0), (0, 3) and 5 then its equation is
\(\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{25}} = 1\)
Question:The foci of \(16{x^2} + 25{y^2} = 400\) are
\(( \pm 3,\;0)\)
\((0,\; \pm 3)\)
\((3,\; - 3)\)
\(( - 3,\;3)\)
Question:Eccentricity of the ellipse \(9{x^2} + 25{y^2} = 225\) is
\(\frac{3}{5}\)
\(\frac{4}{5}\)
\(\frac{9}{{25}}\)
\(\frac{{\sqrt {34} }}{5}\)
Question:The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is
\(5{x^2} - 9{y^2} = 180\)
\(9{x^2} + 5{y^2} = 180\)
\({x^2} + 9{y^2} = 180\)
\(5{x^2} + 9{y^2} = 180\)
Question:In an ellipse the distance between its foci is 6 and its minor axis is 8. Then its eccentricity is
\(\frac{1}{{\sqrt {52} }}\)
\(25{x^2} + 144{y^2} = 900\)
Question:The co-ordinates of the foci of the ellipse \(3{x^2} + 4{y^2} - 12x - 8y + 4 = 0\) are
(1, 2), (3, 4)
(1, 4), (3, 1)
(1, 1), (3, 1)
(2, 3), (5, 4)
Question:The eccentricity of the curve represented by the equation \({x^2} + 2{y^2} - 2x + 3y + 2 = 0\) is
0
1/2
\(1/\sqrt 2 \)
\(\sqrt 2 \)
Question:If any tangent to the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\)cuts off intercepts of length h and k on the axes, then \(\frac{{{a^2}}}{{{h^2}}} + \frac{{{b^2}}}{{{k^2}}} = \)
1
Question:If the line \(y = mx + c\)touches the ellipse \(\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1\), then \(c = \)
\( \pm \sqrt {{b^2}{m^2} + {a^2}} \)
\( \pm \sqrt {{a^2}{m^2} + {b^2}} \)
\( \pm \sqrt {{b^2}{m^2} - {a^2}} \)
\( \pm \sqrt {{a^2}{m^2} - {b^2}} \)
Question:The value of \(\lambda \), for which the line \(2x - \frac{8}{3}\lambda y = - 3\) is a normal to the conic \({x^2} + \frac{{{y^2}}}{4} = 1\) is
\(\frac{{\sqrt 3 }}{2}\)
\(\frac{1}{2}\)
\( - \frac{{\sqrt 3 }}{2}\)
\(\frac{3}{8}\)
Question:The pole of the straight line \(x + 4y = 4\) with respect to ellipse \({x^2} + 4{y^2} = 4\) is
(1, 4)
(1, 1)
(4, 1)
(4, 4)
Question:The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is
\(25{x^2} - 144{y^2} = 900\)
\(144{x^2} - 25{y^2} = 900\)
\(144{x^2} + 25{y^2} = 900\)
Question:The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, -2). The equation of the hyperbola is
\(\frac{4}{{49}}{x^2} - \frac{{196}}{{51}}{y^2} = 1\)
\(\frac{{49}}{4}{x^2} - \frac{{51}}{{196}}{y^2} = 1\)
\(\frac{4}{{49}}{x^2} - \frac{{51}}{{196}}{y^2} = 1\)
Question:The locus of the centre of a circle, which touches externally the given two circles, is
Circle
Parabola
Hyperbola
Ellipse
Question:The foci of the hyperbola \(2{x^2} - 3{y^2} = 5\), is
\(\left( { \pm \frac{5}{{\sqrt 6 }},\;0} \right)\)
\(\left( { \pm \frac{5}{6},\;0} \right)\)
\(\left( { \pm \frac{{\sqrt 5 }}{6},\;0} \right)\)
Question:Centre of hyperbola \(9{x^2} - 16{y^2} + 18x + 32y - 151 = 0\) is
(1, –1)
(–1, 1)
(–1, –1)
Question:The equation of the hyperbola whose foci are (6, 4) and (-4, 4) and eccentricity 2 is given by
\(12{x^2} - 4{y^2} - 24x + 32y - 127 = 0\)
\(12{x^2} + 4{y^2} + 24x - 32y - 127 = 0\)
\(12{x^2} - 4{y^2} - 24x - 32y + 127 = 0\)
\(12{x^2} - 4{y^2} + 24x + 32y + 127 = 0\)
Question:The equation of the tangent to the hyperbola \(2{x^2} - 3{y^2} = 6\)which is parallel to the line \(y = 3x + 4\), is
\(y = 3x + 5\)
\(y = 3x - 5\)
\(y = 3x + 5\) and \(y = 3x - 5\)
Question:The locus of the point of intersection of any two perpendicular tangents to the hyperbola is a circle which is called the director circle of the hyperbola, then the equation of this circle is
\({x^2} + {y^2} = {a^2} + {b^2}\)
\({x^2} + {y^2} = {a^2} - {b^2}\)
\({x^2} + {y^2} = 2ab\)
Question:Let E be the ellipse \(\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1\) and C be the circle \({x^2} + {y^2} = 9\). Let P and Q be the points (1, 2) and (2, 1) respectively. Then
Q lies inside C but outside E
Q lies outside both C and E
P lies inside both C and E
P lies inside C but outside E
Question:The length of the chord of the parabola \({y^2} = 4ax\) which passes through the vertex and makes an angle \(\theta \) with the axis of the parabola, is
\(4a\cos \theta \,{\rm{cose}}{{\rm{c}}^2}\,\theta \)
\(4a{\cos ^2}\theta \,{\rm{cosec}}\,\theta \)
\(a\cos \theta \,{\rm{cose}}{{\rm{c}}^2}\,\theta \)
\(a{\cos ^2}\theta \,{\rm{cosec}}\,\theta \)
Question:The locus of the point of intersection of lines \((x + y)t = a\) and \(x - y = at\), where t is the parameter, is
A circle
An ellipse
A rectangular hyperbola
Question:The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is \(\sqrt 2 \), is
\({x^2} - {y^2} = 16\)
\({x^2} - {y^2} = 32\)
\({x^2} - 2{y^2} = 16\)
\({y^2} - {x^2} = 16\)
Question:The eccentricity of the hyperbola \(\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{{25}} = 1\) is
3/4
3/5
\(\sqrt {41} /4\)
\(\sqrt {41/5} \)
Question:The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8
\(\frac{{{x^2}}}{{12}} - \frac{{{y^2}}}{4} = 1\)
\(\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{12}} = 1\)
\(\frac{{{x^2}}}{8} - \frac{{{y^2}}}{2} = 1\)
\(\frac{{{x^2}}}{{16}} - \frac{{{y^2}}}{9} = 1\)